DAMASK_EICMD/processing/post/addStrainTensors.py

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#!/usr/bin/env python
# -*- coding: UTF-8 no BOM -*-
import os,sys,string
import numpy as np
from collections import defaultdict
from optparse import OptionParser
import damask
scriptID = string.replace('$Id$','\n','\\n')
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scriptName = os.path.splitext(scriptID.split()[1])[0]
def operator(stretch,strain,eigenvalues):
''' Albrecht Bertram: Elasticity and Plasticity of Large Deformations An Introduction (3rd Edition, 2012), p. 102 '''
return {
'V#ln': np.log(eigenvalues) ,
'U#ln': np.log(eigenvalues) ,
'V#Biot': ( np.ones(3,'d') - 1.0/eigenvalues ) ,
'U#Biot': ( eigenvalues - np.ones(3,'d') ) ,
'V#Green': ( np.ones(3,'d') - 1.0/eigenvalues/eigenvalues) *0.5,
'U#Green': ( eigenvalues*eigenvalues - np.ones(3,'d')) *0.5,
}[stretch+'#'+strain]
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# --------------------------------------------------------------------
# MAIN
# --------------------------------------------------------------------
parser = OptionParser(option_class=damask.extendableOption, usage='%prog options [file[s]]', description = """
Add column(s) containing given strains based on given stretches of requested deformation gradient column(s).
""", version = scriptID)
parser.add_option('-u','--right',
dest = 'right',
action = 'store_true',
help = 'material strains based on right Cauchy--Green deformation, i.e., C and U')
parser.add_option('-v','--left',
dest = 'left',
action = 'store_true',
help = 'spatial strains based on left Cauchy--Green deformation, i.e., B and V')
parser.add_option('-0','--logarithmic',
dest = 'logarithmic',
action = 'store_true',
help = 'calculate logarithmic strain tensor')
parser.add_option('-1','--biot',
dest = 'biot',
action = 'store_true',
help = 'calculate biot strain tensor')
parser.add_option('-2','--green',
dest = 'green',
action = 'store_true',
help = 'calculate green strain tensor')
parser.add_option('-f','--defgrad',
dest = 'defgrad',
action = 'extend',
metavar = '<string LIST>',
help = 'heading(s) of columns containing deformation tensor values [%default]')
parser.set_defaults(right = False,
left = False,
logarithmic = False,
biot = False,
green = False,
defgrad = ['f'],
)
(options,filenames) = parser.parse_args()
stretches = []
strains = []
if options.right: stretches.append('U')
if options.left: stretches.append('V')
if options.logarithmic: strains.append('ln')
if options.biot: strains.append('Biot')
if options.green: strains.append('Green')
if options.defgrad == None:
parser.error('no data column specified.')
# --- loop over input files -------------------------------------------------------------------------
if filenames == []: filenames = [None]
for name in filenames:
try:
table = damask.ASCIItable(name = name,
buffered = False)
except: continue
table.croak('\033[1m'+scriptName+'\033[0m'+(': '+name if name else ''))
# ------------------------------------------ read header ------------------------------------------
table.head_read()
# ------------------------------------------ sanity checks ----------------------------------------
items = {
'tensor': {'dim': 9, 'shape': [3,3], 'labels':options.defgrad, 'column': []},
}
errors = []
remarks = []
for type, data in items.iteritems():
for what in data['labels']:
dim = table.label_dimension(what)
if dim != data['dim']: remarks.append('column {} is not a {}...'.format(what,type))
else:
items[type]['column'].append(table.label_index(what))
for theStretch in stretches:
for theStrain in strains:
table.labels_append(['{}_{}({}){}'.format(i+1, # extend ASCII header with new labels
theStrain,
theStretch,
what if what != 'f' else '') for i in xrange(9)])
if remarks != []: table.croak(remarks)
if errors != []:
table.croak(errors)
table.close(dismiss = True)
continue
# ------------------------------------------ assemble header --------------------------------------
table.info_append(scriptID + '\t' + ' '.join(sys.argv[1:]))
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table.head_write()
# ------------------------------------------ process data ------------------------------------------
stretch = {}
outputAlive = True
while outputAlive and table.data_read(): # read next data line of ASCII table
for column in items['tensor']['column']: # loop over all requested defgrads
F = np.array(map(float,table.data[column:column+items['tensor']['dim']]),'d').reshape(items['tensor']['shape'])
(U,S,Vh) = np.linalg.svd(F) # singular value decomposition
R = np.dot(U,Vh) # rotation of polar decomposition
stretch['U'] = np.dot(np.linalg.inv(R),F) # F = RU
stretch['V'] = np.dot(F,np.linalg.inv(R)) # F = VR
for theStretch in stretches:
stretch[theStretch] = np.where(abs(stretch[theStretch]) < 1e-12, 0, stretch[theStretch]) # kill nasty noisy data
(D,V) = np.linalg.eig(stretch[theStretch]) # eigen decomposition (of symmetric matrix)
neg = np.where(D < 0.0) # find negative eigenvalues ...
D[neg] *= -1. # ... flip value ...
V[:,neg] *= -1. # ... and vector
for i,eigval in enumerate(D):
if np.dot(V[:,i],V[:,(i+1)%3]) != 0.0: # check each vector for orthogonality
V[:,(i+1)%3] = np.cross(V[:,(i+2)%3],V[:,i]) # correct next vector
V[:,(i+1)%3] /= np.sqrt(np.dot(V[:,(i+1)%3],V[:,(i+1)%3].conj())) # and renormalize (hyperphobic?)
for theStrain in strains:
d = operator(theStretch,theStrain,D) # operate on eigenvalues of U or V
eps = (np.dot(V,np.dot(np.diag(d),V.T)).real).reshape(9) # build tensor back from eigenvalue/vector basis
table.data_append(list(eps))
# ------------------------------------------ output result -----------------------------------------
outputAlive = table.data_write() # output processed line
# ------------------------------------------ output finalization -----------------------------------
table.close() # close ASCII tables